Playful Math Education Carnival 97

Did you know 97 is an emirp?
Did you know 97 is an emirp? It’s prime both forward and backward! What other emirps can you find?

Welcome to the 97th edition of the Math Teachers At Play math education blog carnival: a monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

A few articles were submitted by their authors, but most were drawn from the immense backlog in my rss reader. If you’d like to see your blog post featured next month, be sure to send it in yourself. Our hosts are busy parents and teachers who have limited time to scour the Internet for goodies.

To add a bit of color, I’ve thrown in several favorites from my newly updated Math with Living Books pages. Some (affiliate) links go to, where you can read descriptions and reviews — but there’s no need to buy. Most of these books should be available through your local library.

Table of Contents

If you’d like to skip directly to your area of interest, click here:

Please: If you enjoy the carnival, would you consider volunteering to host sometime this year? Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn, please speak up!

And now, let the mathematical fun begin!

Pinczes-A Remainder of One

When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade.

Talking Math with Kids

  • Crystal Wagner (@Tri_Learning) shares several Math Games to Play in the Car: “Or maybe you are waiting in line at the grocery store or doctor’s appointment. Turn these times of waiting into learning opportunities.”
  • Christopher Danielson (@Trianglemancsd) shows how The sequence machine can launch math conversations with older students: “Now you can generate number sequences, without being distracted by the multiplication facts.”


Help inspire your kids to try writing their own unique problems. Includes a wide range of math topics and concepts: money and time, fractions, percentages, geometry, logic, and multi-step problem solving.

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Continue reading Playful Math Education Carnival 97

FAQ: Lifelong Learning for Parents

“I’m so tired of being ignorant about math. I can memorize rules and do calculations, but if I miss a step the numbers make no sense at all, and I can’t spot what went wrong. Another struggle I have is keeping everything organized in my mind. When I learn a new concept or strategy, I easily forget it. My son is only a toddler now, but as he grows up, I don’t want to burden him with my own failures. Where should I start?”

As a first step, convince yourself that math is interesting enough to learn on its own merits, because parental guilt will only carry you so far. Start with Steven Strogatz’s “Elements of Math” series from The New York Times, or pick up his book The Joy of x.

As a next step, reassure yourself that elementary math is hard to understand, so it’s not strange that you get confused or don’t know how to explain a topic. Get Liping Ma’s Knowing and Teaching Elementary Mathematics from the library or order a used copy of the first edition. Ma examines what it means to understand math and to clearly explain it to others.

Don’t rush through the book as if it were a novel. There are four open-ended questions, each at the beginning of a chapter, after which several possible answers are analyzed. When you read one of these questions, close the book. Think about how you would answer it yourself. Write out a few notes, explaining your thoughts as clearly as you can. Only then, after you have decided what you would have said, read the rest of that section.

Don’t worry if you can’t understand everything in the book. Come back to it again in a couple of years. You’ll be surprised how much more you learn.


Books for Parents and Teachers

To build up your own understanding of elementary arithmetic, the Kitchen Table Math series by Chris Wright offers explanations and activities you can try with your children.

If you want more detailed guidance in understanding and explaining each stage of elementary mathematics, you can pick up a textbook designed for teachers in training. I like the Parker & Baldridge Elementary Mathematics for Teachers books and the Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction series. The two series are completely different, but they complement each other well. Check out the sample chapters from the publishers’ websites to see which one you prefer.

Discover more great books on my Living Math Books for Parents and Other Teachers page.

Focus on Relationships

As you learn, focus on how the math concepts relate to each other. Then the more you learn, the easier you will find it to connect things in your mind and to grasp new ideas.

You might want to keep a math journal about the things you are learning. When you write something down, that helps you remember it, even if you never look back at the journal. But if your mind goes blank and you think, “I know I studied that,” the journal gives you a quick way to review. Make it even easier to flip back through by writing the topic you are studying in the top margin of each page.

When you run into a new vocabulary word, draw a Frayer Model Chart and fill in all the sections. The Frayer Model provides a way to organize information about a new vocabulary word or math concept.


And if you read something that’s particularly helpful, you may want to turn to the back page of your journal and start a quick-reference section.

Always Ask Why!

Find a fellow-learner to encourage you on your journey. Bouncing ideas off a friend is a great way to learn. You might want to join the parents and teachers who are learning math together at the Living Math Forum.

And here is the most important piece of advice I can offer. Your slogan must be the one used by the Chinese teachers Liping Ma interviewed: “Know how, and also know why.”

Always ask why the rules you learn in math work. Don’t stop asking until you find someone who can explain it in a way that makes sense to you. When you struggle with a concept and conquer it, it will make you free. You don’t have to be afraid of it anymore.

Know how, and also know why.

Click for details about Let's Play Math bookThis post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Multiplication Is Not Repeated Addition: Update

Multiplication Is Not Repeated Addition: Update[Photo “Micah and Multiplication” by notnef via Flickr (CC-BY 2.0).]

Some Internet topics are evergreen. I noticed that my old Multiplication Is Not Repeated Addition post has been getting new traffic lately, so I read through the article again. And realized that, even after all those words, I still had more to say.

So I added the following update to clarify what seemed to me the most important point.

I’d love to hear your thoughts! The comment section is open down below . . .

Language Does Matter

Addition: addend + addend = sum. The addends are interchangeable. This is represented by the fact that they have the same name.

Multiplication: multiplier × multiplicand = product. The multiplier and multiplicand have different names, even though many of us have trouble remembering which is which.

  • multiplier = “how many or how much”
  • multiplicand = the size of the “unit” or “group”

Different names indicate a difference in function. The multiplier and the multiplicand are not conceptually interchangeable. It is true that multiplication is commutative, but (2 rows × 3 chairs/row) is not the same as (3 rows × 2 chairs/row), even though both sets contain 6 chairs.

A New Type of Number

In multiplication, we introduce a totally new type of number: the multiplicand. A strange, new concept sits at the heart of multiplication, something students have never seen before.

The multiplicand is a this-per-that ratio.

A ratio is a not a counting number, but something new, much more abstract than anything the students have seen up to this point.

A ratio is a relationship number.

In addition and subtraction, numbers count how much stuff you have. If you get more stuff, the numbers get bigger. If you lose some of the stuff, the numbers get smaller. Numbers measure the amount of cookies, horses, dollars, gasoline, or whatever.

The multiplicand doesn’t count the number of dollars or measure the volume of gasoline. It tells the relationship between them, the dollars per gallon, which stays the same whether you buy a lot or a little.

By telling our students that “multiplication is repeated addition,” we dismiss the importance of the multiplicand. But until our students wrestle with and come to understand the concept of ratio, they can never understand multiplication.

For Further Investigation

nunes-doingmathIf you’re interested in digging deeper into how children learn addition and multiplication, I highly recommend Terezina Nunes and Peter Bryant’s book Children Doing Mathematics.

To learn about modeling multiplication problems with bar diagrams, check out the Mad Scientist’s Ray Gun model of multiplication:

And here is an example of the multiplication bar diagram in action:

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Amazon Bestseller Today

Bookselling stats rise and fall like a roller-coaster, but the top of the curve is always fun. Today Let’s Play Math hit the Top Ten in homeschooling (“parent participation in education”) at


Update: Top 25 in STEM Resources

I noticed the “STEM Education” category at Amazon, so I updated my book’s keywords. And the Let’s Play Math paperback zipped into the Top 25!


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Let’s Play Math FAQs: Introduction

I’ll let you in on a secret about teaching: there is no place in the world where it rolls along smoothly without problems. Only in articles and books can that happen.

—Dr. Ruth Beechick
You Can Teach Your Child Successfully

Learning math is an adventure into the unknown. The ideas we adults take for granted are a wild, unexplored country to our children. Like any traveler in a strange land, they will stumble over rocky places and meet with unexpected detours.

Whenever I visit a parenting forum, I feel compassion for the families who are struggling with math. No other school subject elicits such depths of frustration and despair:

  • I’ve explained until I’m hoarse, and she still doesn’t get it. Help!! I want to pull my hair out.
  • My child is not a mathy person at all. Now he’s convinced that he’s “dumb.”
  • She says she can’t do it. She says she hates math. She says she can’t think. She hits her head and pounds her fists in frustration. I am so tired of fighting over math Every. Single. Day.
  • The problem is not him … It’s me. I am a failure at math.
  • I am sooooo struggling to teach my daughter math. Please, does anybody else deal with this? I will try anything!

Let's Play Math FAQs: Introduction

Yes, There IS Hope!

Solving the problems of math education is not easy. Situations have built up over years, so they will take time to resolve.

But children are resilient, so improvement may not take as long as you fear.

No matter how much your family has struggled, there is hope. If children can get over the “I’m no good at math” mental block, they can learn all of elementary arithmetic in one school year of determined study.

Does that seem unbelievable? Consider Daniel Greenberg’s experience:

Math as a Second Language

If math feels like a strange and dangerous wilderness to your children, you may need an experienced guide to lead you through the rough spots. For arithmetic, try Herb Gross’s Math as a Second Language webpages:

For upper-level math topics, explore Murray Bourne’s Interactive Mathematics pages or take a look at Kalid Azad’s Better Explained site:

About the Let’s Play Math FAQ Series

The questions in this blog post series will be based on actual forum discussions, though I always change the details, removing anything that might identify the families involved.

We’ll look at a variety of struggles with math, such as:

  • Lifelong Learning for Parents
  • Primary Level Problems
  • Middle Grade Mishaps
  • The Agonies of Algebra
  • Gaps and Standardized Testing

The questions will cover a wide range of common frustrations that resonate with anyone who has tried to explain an abstract idea to a confused child. Some questions apply specifically to homeschool math, yet non-homeschooling families can use many of the resources I recommend to supplement their children’s schoolwork or to keep skills sharp over the summer.

Special Cases

In my FAQ post answers, I will assume you are working with children of normal intelligence, facing the mental strengths and weaknesses that are common to us all. The human brain is not designed for working with abstraction, so most people find math difficult.

But some face additional hardship because their minds are unable to process numbers and related concepts. If you suspect one or more of your children may struggle with a learning disability, please have them tested and get advice from someone who can help you learn to deal with their special circumstances.

Auditory or vision problems, undiagnosed food allergies, and a family crisis or other emotional strain may also affect a child’s concentration. Sometimes, the best way to help your children learn math is to let it go and deal with other issues first.

To be continued . . .

Click for details about Let's Play Math bookThis post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Did You Get Your Playful Math Snacks?

Circumferències de FordMy April “Let’s Play Math” newsletter went out early this morning to everyone who signed up for Tabletop Academy Press math updates. This month’s issue celebrated the 200th anniversary of the Farey Sequence.

The Farey Sequence was described in 1816 by English geologist John Farey, who was disparaged by the famous mathematical snob* G.H. Hardy as “at the best an indifferent mathematician.”

“I rather like the idea that the Farey Sequences are named after someone who noticed a pattern and asked a question — and not even the first person to notice the pattern, ask the question, or provide the answer. As math teachers, we teach plenty of indifferent mathematicians who wake up when they experience the joy of discovering something that is new to them, not necessarily new to the whole world.”

— Debra K. Borkovitz,
Farey Fraction Visual Patterns

If you’re a subscriber but didn’t see your newsletter, check your Updates or Promotions tab (in Gmail) or your Spam folder. And to make sure you get all the future newsletters, add “Denise at Tabletop Academy Press” [denise.gaskins @ tabletop academy press .com, without spaces] to your contacts or address book.

And if you missed this month’s edition, no worries—‌there will be more playful math snacks next month. Click the link below to sign up today, and we’ll send you our free math and writing booklets, too!

As a Bonus: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

* See A Mathematician’s Apology Revisited by W.W. Sawyer.